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In approximation theory, a Haar space or Chebyshev space is a finite-dimensional subspace V {\displaystyle V} of C {\displaystyle {\mathcal {C}}} , where X {\displaystyle X} is a compact space and K {\displaystyle \mathbb {K} } either the real numbers or the complex numbers, such that for any given f ∈ C {\displaystyle f\in {\mathcal {C}}} there is exactly one element of V {\displaystyle V} that approximates f {\displaystyle f} "best", i.e. with minimum distance to f {\displaystyle f} in supremum norm.
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